Well, the procedure is essentially identical to converting between rectangular and polar coordinates on the good ol' real plane, so if that's where you're having trouble, you can pick up one of your old textbooks and review.

I'm having a hard time rewriting from one form to another, carthesian - polar and so on.

As Hurkyl said, just think of the good ole plane here.

Examples:
Suppose that a complex number z is given by:
z=a+ib
where a,b are real numbers, and i the imaginary unit.
Then, multiply z with 1 in the following manner:
[tex]z=\frac{\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}(a+ib)={\sqrt{a^{2}+b^{2}}}(\frac{a}{\sqrt{a^{2}+b^{2}}}+i\frac{b}{\sqrt{a^{2}+b^{2}}})[/tex]
Find the angle [tex]\theta[/tex] that is the solution of the system of equations:
[tex]\frac{a} {\sqrt{a^{2}+b^{2}}}=\cos\theta,\frac{b}{\sqrt{a^{2}+b^{2}}}=\sin\theta[/tex]
Thus, defining [tex]|z|={\sqrt{a^{2}+b^{2}}}[/tex], we get:
[tex]z=|z|(\cos\theta+i\sin\theta)=|z|e^{i\theta}[/tex]
by definition of the complex exponential.

I can only give you one tip:
(i) Get familiar with graphical interpretation of the sine and cosine in a circle.
(ii) Really try to understand the formula by examining the drawing of a complex number (like in the link above).